1. Field of the Invention
The present invention relates to an apparatus for adjusting frequency characteristic and Q factor of a low pass filter and a method thereof; and, more particularly, to an apparatus for adjusting frequency characteristic and Q factor of a low pass filter that can improve filtering efficiency of the low pass filter (LPF) by adjusting the frequency characteristic and the Q factor according to a desired filtering function and a method thereof. The frequency characteristic and the Q factor are changed due to the variation of capacitance and resistance occurring when the LPF is implemented by an application specific integrated circuit (ASIC).
This work was supported by the Information Technology (IT) research and development program of the Korean Ministry of Information and Communication (MIC) and the Korean Institute for Information Technology Advancement (IITA) [2006-S-071-01, “Development of UWB Solution for High Speed Multimedia Transmission”].
2. Description of Related Art
Generally, a variety of elements are needed to construct a radio frequency (RF) transceiver which is implemented by an application of specific integrated circuit (ASIC). Among such elements, a low pass filter (LPF) for passing desired signal and eliminating undesired signal from received signal is an important part to determine the quality of the received signal.
However, values of resistors, capacitors and inductors included in the LFP are changed due to characteristics of ASIC fabrication. The Q factor and frequency characteristic, which are important performances of the LPF, are changed due to the above variation. Thus, characteristics of pass band and stop band of the LPF are changed so that the received signal is distorted.
Also, when a transceiver of a communication system is designed, the LPF is hard to design due to neighbor signals. Therefore, in order to improve characteristics of a receiver the broadness of the passband and insertion loss of the stopband must be enhanced by utilizing the frequency characteristic and the Q factor characteristic.
The principle of adjusting the frequency characteristic and the Q factor characteristic will be described hereinafter.
Generally, differential 2nd-order transfer function of the LPF, i.e., input-to-output ratio of the LPF, is expressed as the following Eq. 1.
                              T          ⁡                      (            s            )                          =                              a            0                                              S              2                        +                                          (                                                      ω                    0                                    /                  Q                                )                            ⁢              S                        +                          ω              0              2                                                          Eq        .                                  ⁢        1            
Herein, a0 is a constant; S means a domain, i.e., jω; ω0 represent a frequency of the pass band; and Q means Q factor.
Herein, ω0 and Q determine a natural mode according to the following Eq. 2.
                              P          1                ,                              P            2                    =                                    -                                                ω                  0                                                  2                  ⁢                  Q                                                      ±                                          jω                0                            ⁢                                                1                  -                                      (                                                                  1                        /                        4                                            ⁢                                              Q                        2                                                              )                                                                                                          Eq        .                                  ⁢        2            
Here, ω0 and Q determine characteristics of the LPF. In FIG. 6, when a value of the transfer function is the maximum value, |T|MAX and ωMAX, the frequency corresponding to |T|MAX, are expressed as the following Eq. 3.
                                          ω            MAX                    =                                    ω              0                        ⁢                                          1                -                                  1                                      2                    ⁢                                          Q                      2                                                                                                          ⁢                                  ⁢                              T            MAX                    =                                                    a                0                            ⁢              Q                                                      ω                0                2                            ⁢                                                1                  -                                      1                                          4                      ⁢                                              Q                        2                                                                                                                                                    Eq        .                                  ⁢        3            
Here, a frequency having a magnitude of 3 dB smaller than the magnitude of TMAX, i.e., 3 dB frequency, is expressed as the following Eq. 4. That is, in the following Eq. 4, the 3 dB frequency can be controlled by adjusting ω0 and Q.
                              ω          1                ,                              ω            2                    =                                                    ω                0                            ⁢                                                1                  +                                      (                                                                  1                        /                        4                                            ⁢                                              Q                        2                                                              )                                                                        ±                                          ω                0                                            2                ⁢                Q                                                                        Eq        .                                  ⁢        4            
Herein, BW=ω1−ω2=ω0/Q. That is, as Q is increased, the bandwidth is decreased, and band-pass filter is getting more selective. That is, desired frequency range and selectiveness can be controlled by adjusting ω0 and Q.
Therefore, a method for adjusting the frequency characteristic and the Q factor of the LPF is needed based on the principle of adjusting the frequency characteristic and the Q factor.